Fresh features from the #1 AI-enhanced learning platform.Try it free
Fresh features from the #1 AI-enhanced learning platformCrush your year with the magic of personalized studying.Try it free
Question

# Credit Card Debt John has a balance of $3000 on his Discover card that charges 1% interest per month on any unpaid balance. John can afford to pay$100 toward the balance each month. His balance each month after making a $100 payment is given by the recursively defined sequence$B_{0}=$3000 \quad B_{n}=1.01 B_{n-1}-100$ Determine John's balance after making the first payment. That is, determine $B_{1}$.

Solution

Verified
Step 1
1 of 2

$\text{\color{#4257b2}We need to determine the first payment term\ (B_{1})\ for the following expression.}$

$\color{Brown}B_{0}=3000\text{\ Dollars}\ \ \ \ \ \ \ \ \ \ \ \ B_{n}=1.01\ B_{n-1}-100$

$\lozenge$\ $\text{\underline{\bf{Solution:}}}$

To get any term, substitute the number of term in the expression which given as follows:

$B_{n}=1.01\ B_{n-1}-100$

$B_{0}=3000$

$B_{1}=1.01\ B_{1-1}-100\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B_{1}=1.01\ B_{0}-100$

$B_{1}=(1.01\cdot3000)-100\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B_{1}=3030-100$

$B_{1}=2930\ \text{Dollars}$

So, the first payment term is \ $2930$\ dollars

## Recommended textbook solutions

#### Thomas' Calculus

14th EditionISBN: 9780134438986 (8 more)Christopher E Heil, Joel R. Hass, Maurice D. Weir
10,144 solutions

#### Calculus: Early Transcendentals

8th EditionISBN: 9781285741550 (5 more)James Stewart
11,085 solutions

#### Calculus: Early Transcendentals

9th EditionISBN: 9781337613927Daniel K. Clegg, James Stewart, Saleem Watson
11,048 solutions

#### Calculus for the AP Course

2nd EditionISBN: 9781464142260 (2 more)Kathleen Miranda, Michael Sullivan
7,557 solutions